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ACT Math Formula Sheet

The ACT gives you ZERO formulas. This program has the full set — geometry, trig, sequences, probability, and logs.

Files (1)
ACTMATH.py1313 bytes
def p(s):print(s)
def w():input("...")
def o1():
 p("=GEOMETRY=")
 p("CIRCLE:")
 p("A=pi*r^2")
 p("C=2*pi*r")
 w()
 p("TRIANGLE:")
 p("A=bh/2")
 p("P=a+b+c")
 w()
 p("TRAPEZOID:")
 p("A=h(b1+b2)/2")
 p("CYLINDER:")
 p("V=pi*r^2*h")
 w()
def o2():
 p("=TRIG=")
 p("SOHCAHTOA:")
 p("sin=opp/hyp")
 p("cos=adj/hyp")
 p("tan=opp/adj")
 w()
 p("LAW SINES:")
 p("a/sinA=")
 p("b/sinB=")
 p("c/sinC")
 w()
 p("LAW COS:")
 p("c2=a2+b2")
 p("-2ab*cosC")
 w()
def o3():
 p("=SEQ/SERIES=")
 p("ARITH nth:")
 p("an=a1+(n-1)d")
 p("SUM n terms:")
 p("S=n(a1+an)/2")
 w()
 p("GEOM nth:")
 p("an=a1*r^(n-1)")
 p("SUM geom:")
 p("S=a1(1-r^n)")
 p("/(1-r)")
 w()
def o4():
 p("=PROBABILITY=")
 p("P(A)=favor/")
 p("total")
 w()
 p("P(A and B)=")
 p("P(A)*P(B)")
 p("(indep)")
 w()
 p("P(A or B)=")
 p("P(A)+P(B)-")
 p("P(A and B)")
 w()
def o5():
 p("=LOGS=")
 p("log_b(x)=y")
 p("=> b^y=x")
 w()
 p("log(mn)=")
 p("log m+log n")
 p("log(m/n)=")
 p("log m-log n")
 w()
 p("log(m^n)=")
 p("n*log m")
 p("CHANGE BASE:")
 p("log_b(x)=")
 p("log(x)/log(b)")
 w()
def menu():
 while True:
  p("=ACT MATH=")
  p("1:GEOMETRY")
  p("2:TRIG")
  p("3:SEQUENCES")
  p("4:PROB")
  p("5:LOGS")
  p("0:EXIT")
  c=input("?>")
  if c=="1":o1()
  elif c=="2":o2()
  elif c=="3":o3()
  elif c=="4":o4()
  elif c=="5":o5()
  elif c=="0":break
menu()
How to use it

The ACT is the test where you're on your own for formulas — they give you nothing. This program bundles the 15-20 formulas that actually appear on the ACT Math section, organized by topic.

Launch ACTMATH from prgm. Open the category matching your current question:

  • 1:GEOMETRY — circle, triangle, trapezoid, cylinder (the four shapes ACT loves)
  • 2:TRIG — SOHCAHTOA, Law of Sines, Law of Cosines
  • 3:SEQUENCES — arithmetic + geometric nth-term and sum formulas
  • 4:PROB — basic probability + and/or rules
  • 5:LOGS — log definition, product/quotient/power rules, change-of-base

Pure reference — no prompts. Flip through between problems.

Example problem

ACT question: In a triangle, sides a=5, b=7, and angle C between them is 60°. Find side c.

This is a Law of Cosines setup.

  1. Run ACTMATH, pick 2:TRIG.
  2. Page through to: c2=a2+b2-2ab*cosC.
  3. Plug in: c² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.
  4. c = √39 ≈ 6.24. ✓

ACT wants you to nail this in under 90 seconds. Having the formula on-screen saves the scratch-work of rederiving it.

TI-84 Plus CE — try before committingoff
TI-84 Plus CE



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Test cases (2)
IDInputsExpected contains
geometry1, , , , 0A=pi*r^2, C=2*pi*r
trig2, , , , 0SOHCAHTOA, sin=opp/hyp